A regular decagon has all its interior angles equal. What is the measure of each interior angle of a regular decagon? Choose the correct answer.

• A. $150°$
• B. $144°$
• C. $120°$
• D. $135°$

Answer: (B)

Verified step by step guidance

1. Recall that a regular polygon has all sides and all interior angles equal. For any polygon with \(n\) sides, the sum of the interior angles is given by the formula: \(\text{Sum of interior angles} = (n - 2) \times 180^\circ\).
2. Identify the number of sides of the polygon. Since the problem states a regular decagon, it has \(n = 10\) sides.
3. Calculate the sum of all interior angles of the decagon by substituting \(n = 10\) into the formula: \((10 - 2) \times 180^\circ\).
4. Since the decagon is regular, each interior angle is equal. To find the measure of each interior angle, divide the total sum of interior angles by the number of sides: \(\frac{(10 - 2) \times 180^\circ}{10}\).
5. Simplify the expression to find the measure of each interior angle of the regular decagon.